Actually, the answer to that question is “yes and no”. Sometimes the characteristics of a mineral, whether in a pure form or in a multi-mineral rock, can be identified from a photo. Unfortunately though, most minerals share visual qualities with many quite different minerals.
This makes it impossible to give specific identifications. Also, some qualities (like translucence, metallic sheen, hardness, reaction to a magnet, crystal form, and others) will or may not be visible in a photo.

Chemical composition is not visible, even in a hand sample. People with practice can often do photo identifications, but even experts will not be able to do it for any but the most common minerals.

Professional and rock-hound experts often can do it, if they know the origin of the mineral or rock. They know what is likely to be found in specific localities and use experience to eliminate wrong possibilities.

So, if you know the location your specimen came from, ask a professional rock-hound like The Crystal Collector.

You can also check out THIS article on Crystal Identification 😉

Another excellent site is Mindat